The most-common is an untucked shirt as the cover garment, with a moisture-wicking undergarment underneath everything. Sometimes, the shirt functioning as the cover garment is open/unbuttoned, and, sometimes, it is closed-front. I like to wear shirts that look OK with the bottom one or two buttons left unbuttoned.
My primary weapon’s default position, for about three decades, was 0300-0330, but recently, has crept a bit forward of 0300. I have experimented with AIWB, but doubt I will go all-in, largely because I would rather reserve the area of the inguinal crease for the occasional large blade.
Edited to add: I am actually in a state of transition. I retired from LEO-ing in 2018, which changes some things which had been important, such as the desire to tote the same weapon system as my duty pistol, during personal time. Plus, my right hand, arm, and shoulder are not aging well, so I appreciate weapons that “clear leather” quicker. Plus, I may be switching to left-side-primary. (I am actually left-handed, naturally, but right-armed, and sufficiently ambidextrous that it made sense to carry big guns on my right hip, way back in 1983, when I established my “primary” carry position.) So, what I type, today, may change within a short time.